4sin^4 (2x) + 3cos (4x) - 1=0

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Так как cos 4x = 1 - 2 sin^2 2x;

4 sin^4 2x + 3 (1 - 2 sin^2 2x) - 1 = 0;

4 sin^4 2x + 3 - 6 sin^ 2x - 1 = 0;

4 sin^4 2x - 6 sin^2 2x + 2 = 0;

2 sin^4 2x - 3 sin^2 2x + 1 = 0;

sin^2 2x = t; - 1 ≤ t ≤ 1;

2 t^2 - 3 t + 1 = 0;

t1 = 1; ⇒ sin^2 2x = 1; ⇒ sin 2x = + - 1; ⇒ 2x = pi/2 + pi*k; ⇒ x = pi + 2 pi*k.

t2 = 1/2; ⇒ sin^2 2x = 1/2; ⇒sin 2x = + - sgrt2/2; 2x = pi/4 + pik/2; ⇒x = pi/2 + pik; k-Z.

б) x = pi; 3 pi/2.